Functional magnetic resonance imaging (fMRI) suffers from many problems that make signal estimation difficult. These include variation in the hemodynamic response across voxels and low signal-to-noise ratio (SNR). We evaluate several analysis techniques that address these problems for event-related fMRI. (1) Many fMRI analyses assume a canonical hemodynamic response function, but this assumption may lead to inaccurate data models. By adopting the finite impulse response model, we show that voxel-specific hemodynamic response functions can be estimated directly from the data. (2) There is a large amount of low-frequency noise fluctuation (LFF) in blood oxygenation level dependent (BOLD) time-series data. To compensate for this problem, we use polynomials as regressors for LFF. We show that this technique substantially improves SNR and is more accurate than high-pass filtering of the data. (3) Model overfitting is a problem for the finite impulse response model because of the low SNR of the BOLD response. To reduce overfitting, we estimate a hemodynamic response timecourse for each voxel and incorporate the constraint of time-event separability, the constraint that hemodynamic responses across event types are identical up to a scale factor. We show that this technique substantially improves the accuracy of hemodynamic response estimates and can be computed efficiently. For the analysis techniques we present, we evaluate improvement in modeling accuracy via 10-fold cross-validation.